Perspective: Maximum Caliber is a General Variational Principle for Dynamical Systems
Publication Date
1-7-2018
Document Type
Article
Organizational Units
Physics and Astronomy
Keywords
Markov processes, Probability theory, Nerve cells, Statistical physics, Information theory entropy, Equilibrium thermodynamics, Thermodynamic properties, Nonequilibrium statistical mechanics, Calculus of variations, Dynamical systems
Abstract
We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager’s reciprocal relations, and Prigogine’s minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.
Publication Statement
Copyright held by author or publisher. User is responsible for all copyright compliance.
Recommended Citation
Dixit, Purushottam D, et al. “Perspective: Maximum Caliber Is a General Variational Principle for Dynamical Systems.” The Journal of Chemical Physics, vol. 148, no. 1, 2018, p. 010901. doi: 10.1063/1.5012990